Mulliken’s approach

Since V b plays a central role in the theory, its determination in the largest possible series of compounds is of great interest. In a two-state model, a simple evaluation of the transition moment, using Mulliken s approach of donor acceptor systems, yields Hush s (1967) equation [38bj ... 

Mulliken s approach is in widespread use for many reasons. First, it is conceptually simple and straightforward. An atomic orbital belongs to the atom on which it is centered. Therefore, any electrons in a particular orbital belong to the atom on which that orbital is centered. This notion is based on a very strong belief that atomic orbital nature persists in molecules. Second, Mulliken population analysis is very easily coded into a computer program and is included in all ab initio and semiempirical packages. When a calculation is run, the user obtains the Mulliken populations by default. Finally, since essentially the birth of modern quantum chemistry use of Mulliken population analysis has gained an almost exalted, if not canonical stature. The Mulliken population analysis has always been reported therefore, it will continue to be used. 

A simple, additive fragmentation approach to the molecular electronic density, proposed by the author, can be used for the construction of electronic densities and density-based shape representations for macromolecules. The simplest of these approaches is motivated by Mulliken s population analysis technique,and can be regarded as a natural generalization of Mulliken s approach a formal population analysis without integration. This method, the Mulliken-Mezey approach, is the simplest realization of a more general, additive fuzzy density fragmentation (AFDF) principle. ... 

In Mulliken s approach [31] the electronegativity Xf of a free atom F in its ground state is defined as the arithmetic average of its first ionization potential Ip and electron affinity Ap, which makes electronegativity a property complementary to Pearson s hardness rjp [39] ... 

When atom-centered basis sets are used, a very simple procedure to assign the electrons among the atoms of the molecule comes from Mulliken s approach [26]. Within this method, the number of electrons assigned to the atom A is given by... 

The authors [33] have elucidated the linear dependence of Ao0 (z-dep) on E for the polyanions by a quantum chemical consideration. A model Hamiltonian approach to the charge transfer (CT) interaction between a polyanion and solvents has been made on the basis of the Mulliken s CT complex theory [34]. 

This rescaling reflects the idea that any increase of electronic charge at a center, as a consequence of an enrichment of the basis functions describing it, is unphysical if, lacking equipoise, atoms bonded to it suffer from poorer basis set descriptions. The parameter introduced in Eq. (8.4) is there to correct this imbalance if we follow Mayer s claim [172,173] that Mulliken s half-and-half partitioning of overlap terms between the concerned atoms should not be tampered with. It is felt that the way depends on the basis sets used for describing atoms k and I deserves attention as part of an effort aimed at letting X.rtsi approach Mulliken s limit A = 1 as closely as possible. 

In a recent study, Curtis and coworkers (34) developed an analysis of electronic coupling in mixed-valence complexes that combines electrochemical results with an extension of Mulliken s theory of donor-acceptor interactions. The approach was applied to class II and near class III complexes. It was found that the degree of electronic coupling in these systems is at least three times that which would be predicted based solely on spectroscopic measurements (Eq. 15 of the Hush model). However, the electronic coupling determined for complexes that were very close to, if not of, class III character was significantly smaller than that predicted by Eq. (16). 

Molecular orbital theory originated from the theoretical work of German physicist Friederich Hund (1896-1997) and its apphcation to the interpretation of the spectra of diatomic molecules by American physical chemist Robert S. MuUiken (1896-1986) (Hund, 1926, 1927a, b Mulliken, 1926, 1928a, b, 1932). Inspired by the success of Heitler and London s approach, Finklestein and Horowitz introduced the linear combination of atomic orbitals (LCAO) method for approximating the MOs (Finkelstein and Horowitz, 1928). The British physicist John Edward Lennard-Jones (1894-1954) later suggested that only valence electrons need be treated as delocalized inner electrons could be considered as remaining in atomic orbitals (Lennard-Jones, 1929). 

The simplest model consists of two centres, one donor (D) and one acceptor (A), separated by a distance I and contains two electrons. Here we consider this simple system to illustrate some general relations between charge transfer, transition intensities and linear as well as non-linear optical polarizabilities. We will show below that the electro-optic parameters and the molecular polarizabilities may be described in terms of a single parameter, c, that is a measure of the extent of coupling between donor and acceptor. Conceptually, this approach is related to early computations on the behaviour of inorganic intervalence complexes (Robin and Day, 1967 Denning, 1995), Mulliken s model for molecular CT complexes (Mulliken and Pearson, 1969) and a two-form/two-state analysis of push-pull molecules (Blanchard-Desce and Barzoukas, 1998). 

Figure 1 shows the linear correlation between F chemical shift and solvent donicity. No relationship exists between chemical shifts and dipole moments or polarizabilities of the solvent molecules. This result is particularly significant in that it shows that the functional approach can be successfully applied even to weak chemical interactions, for example, to interactions that are usually considered as being due to Van der Waals forces or intermolecular forces in the sense of Mulliken s theory. 

The 7/ / terms are the Coulomb functions introduced in eq.(104), P are the relaxed (i.e. polarized by the solvent in a self-consistent manner) elements of the density matrix P = CnC, and F are the elements of the in vacuo Fock matrix, in the form used in the semiempirical approach, but referred to the relaxed P matrix. The charges qk are drawn from P, according to the Mulliken s rules, or according to a new definition given by... 

In 1934, Mulliken proposed a different electronegativity scale based upon the average of the ionization potential in volts (IP X X + e ) and the electron affinity (EA X + e" X ) of the gas-phase atoms. This approach is more in character with Mulliken s MO approach since IP reflects the energy of the highest occupied molecular orbital (HOMO) while the EA has a relationship to the energy of the lowest unoccupied molecular orbital (LUMO). Not surprisingly, there has been continued debate ever since over the superiority of these two and numerous later electronegativity scales. 

In Mulliken s valence-bond approach the donor-acceptor complex, DA, is considered to be described by a wave function which may be written... 

Mulliken s interest in the electronic levels in molecules in the 1920s was stimulated by suggestions that their molecular spectra bore similarities to atomic spectra and definite relationships could be discerned for isosteric molecules. He found that the spectroscopic analogy between isosteric molecules could be extended to atoms with the same number of electrons, and this relatirmship was to lead subsequently to the united atom approach. He and Birge classified the electronic states in diatomic molecules using the same Russell-Saunders classification used previously for atomic states. Himd s theoretical analysis [ 149,162-166] of the nature of electronic states in molecules therefore proved to be timely for Mulliken and led him to publish [167-171] a summary of the theory and provide extra experimental evidence supporting it. In the molecular orbital theory Hund showed how the concept of atomic orbitals and the mathematical procedures developed to define them could... 

Mulliken s method, like that of Pauling, tends to overestimate the ENs of fluorine, oxygen and nitrogen, and essentially for the same reason neglecting the inter-electron repulsion (see above). The quantum-mechanical approach was further developed using the electron density functional theory [394,395], according to which EN is the negative chemical potential p.. 

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